Ais was born 1000 years ago. She lived in that era for the first six years of her life, with her parents, potential other relatives, and her parents' friends, until the Black Dragon descended on her home and killed everyone, though her dad managed to put out its eye. Somehow, during that, she was thrown forward in time. The exact means is still uncertain, but she was either sent forward by some sort of portal, or magically frozen. In either case, she arrived in the modern era at the same age she left the ancient days in; six. She then spent the next ten years in Loki Familia as an adventurer.

She is sixteen years old.

What Rabid said is accurate except that she was seven, not six. So, she has been an adventurer with Loki familia for about 9 years now. Also, Aria is likely alive since Ais's goal is to "take her back". We don't know what state she is in though. It is a common theory that the dragon absorbed her and her power somehow which is why the dragon is so strong and why Ais will likely be key in defeating it.

I have always understood that she was six when she was sent forward, and turned seven within the first few months of being an adventurer.

She was seven when she registered in the Guild, which she did the same day she got her falna.

Counterpoint: In SO10, Riveria specifically says that Ais leveled up to Level 2 nine years ago. Ais leveled up after one year in LF. Therefore, Ais has been in LF for 10 years, having joined at six.

I checked and Riveria indeed said that in SO10. But it's also true Ais was said to be seven when she registered in SO9. The math doesn't add up.

Perhaps. Or perhaps not. How long was Ais with LF before she finally convinced Loki to give her Falna? And did she even tell them the truth about her age in the first place?

Probably a mistake that statement in SO10. In DM4 and SO5 it is stated it was an eight years old Ais who reached Level 2 in just a year. In EF it is also stated Ais still doesn't have ten years of career to her name.

And again, SO9 shows the scene explicity. Riveria takes Ais to the Guild, and when she has to write in her registration sheet she puts she is seven years old. At the very least Ais' adventurer career undeniably started when she was already seven years old. That much is made pretty clear.

You could argue she arrived way earlier to the present, and hence was six when she did. There certainly isn't anything denying that, but it is just as certain that there is no evidence to support the idea.